Question

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in figure. How much paper of each shade has been used in it?

Answer 1

ABCD is square
$\therefore$ Both diagonals are equal $=32cm$ (each) also diagonals bisect each other at right angle
$\therefore AC=32cm\&BP=PD=\frac{32}{2}=16cm$
$\therefore$ area of $\left(ABC\right)=ar\left(ADC\right)$
$=\frac{1}{2}\left(32\right)\times 16=256c{m}^2$
and area of $\Delta DEF$
$=\sqrt{s(s-a)(s-b)(s-c)},s=\frac{8+6+6}{2}=10cm$
$=\sqrt{10(10-8)(10-6{)}^2}$
$=8\sqrt{5}c{m}^2=8\times 2.236=17.88c{m}^2$
$\therefore$ required areas are $256c{m}^2,256c{m}^2,17.88c{m}^2$